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Two firms produce a good q and receive a price p = 10 for the good....

Two firms produce a good q and receive a price p = 10 for the good. Firm 1 has marginal costs MC1 = q while firm 2 has marginal costs MC2 = 2q. The production of each unit causes marginal external damage of 2 monetary units. The government wants to limit production with a cap and trade system. The total cap is divided among firms as production quota. Each firm can only produce up to its production quota. However, they can trade quota in order to expand production. What is the equilibrium quota price if the cap is set optimally?

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